|
%I #31 Dec 02 2018 02:45:12
%S 1,4,6,21,80,4151,6982,269563,779693,834365,16176645,19770092,
%T 41049539,228612936,1950787140,2404785364,3095996836,5236785750
%N Number of consecutive composites beginning with the first, to be added to obtain a power.
%C All powers are squares with the exception of 3^3 for a(2) and 6^9 for a(6). I conjecture these are the only nonsquare powers.
%C a(19) > 10^10. - _Zak Seidov_, Jul 06 2013
%F {n: A053767(n) in A001597}. - _Zak Seidov_, Jul 06 2013
%e Considering 1 not to be prime and not to be composite, first composite is 4 which is 2^2. And the sum of the first four composites is 4 + 6 + 8 + 9 = 27 = 3^3.
%p # see A001597 for isA001597
%p for n from 1 do
%p if isA001597(A053767(n) ) then
%p print(n) ;
%p end if;
%p end do: # _R. J. Mathar_, Jul 08 2013
%o (PARI) : n=10^7;v=vector(n);i=0;for(a=2,n,if(isprime(a),next,i++;v[i]=a));k=0;for(j=1,i,k=k+v[j];if(ispower(k,,&n),print1([k,n,j]," ")))
%Y Cf. A001597, A002808, A053767, A141092.
%K nonn,more
%O 1,2
%A _Robin Garcia_, Jul 04 2013
%E a(11) - a(18) from _Zak Seidov_, Jul 06 2013
|
